Heat the oven to 400°F with a rack in the middle position. Place the chicken in a bowl and chill in the freezer about 15 minutes.
Meanwhile, place the Parmesan in the food processor and pulse until it resembles coarse breadcrumbs, about 15 one-second pulses. Add the bread pieces and pulse until the mixture forms fine breadcrumbs, 15 to 20 one-second pulses. Remove 3/4 cup (65 grams) of the breadcrumb mixture, transfer to a pie plate or shallow bowl, and reserve for later. Add the parsley, basil, oregano, black pepper, lemon zest, and nutmeg to the food processor bowl and pulse until finely chopped, 8 to 10 one-second pulses. Transfer the herbed breadcrumb mixture to a large bowl.
Remove the chicken from the freezer and pulse in the food processor until it resembles a coarse, medium grind, 8 to 10 one-second pulses. Transfer to the bowl with the herbed breadcrumbs, along with the garlic powder and salt. Using your hands, combine until everything is well incorporated, trying not to overwork the meat.
Divide the meatball mixture into 18 to 20 meatballs, each weighing about 1 ounce (28 grams), and roll them in the reserved plain breadcrumb mixture. Place on a half sheet pan.
Heat 3 tablespoons of the olive oil in an oven-safe, 11-inch, straight-sided sauté pan over medium heat. When the oil is shimmering, place half of the meatballs in the skillet and cook until well browned on two sides, 2 to 3 minutes per side. Return to the half sheet pan and repeat with the second half of the meatballs, adding 1 more tablespoon of oil if needed. Remove the pan from the heat to cool for 1 minute.
Add the wine to the now-empty pan. Return to medium heat and bring to a simmer. Cook, scraping up the browned bits from the bottom of the pan, until the wine is reduced by about half, about 2 minutes. Add the Red Sauce and reserved tomato liquid and stir well to combine. Remove from the heat. Return all of the meatballs to the pan and gently stir the meatballs to cover with sauce. Combine the grated mozzarella and fontina in a small bowl and sprinkle the mixture over the top of the meatballs.
Bake until the meatballs are cooked through and the cheese is melted and bubbly, 12 to 15 minutes. Let cool for about 5 minutes before serving over cooked pasta, on top of crispy bread, or inside a hoagie roll.